Intermediate Value Theorem to show that there is a root in a given equation/interval

Question: Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

37.

x^4 + x - 3 = 0, (1,2)

What do I do for this question? Do I plug in 1 and 2 and try to estimate something in the middle, like I don't get what it is asking in the first place. Like what does "a root of the given equation in the specified interval" mean?

Any help would be greatly appreciated!
Thanks in advance!

September 20th 2009, 11:28 AM

Arturo_026

Yes, plug your x values and according to IVT if one is possitive and the other is negative, than there has to be a root between thos numbers...ofcourse since the function is a polynomial therefore it's continuous.

September 20th 2009, 11:35 AM

s3a

So the question is not asking me to show "the root of the given equation," right? But what does that mean exactly?

September 20th 2009, 11:37 AM

Arturo_026

Quote:

Originally Posted by s3a

So the question is not asking me to show "the root of the given equation," right? But what does that mean exactly?

A root is also know as a zero, or where the graph crosses the x-axis.
So u just have to substitute x for your given values and checkk their signs.